Step-by-step explanation:
Changes made to your input should not affect the solution:
(1): "q2" was replaced by "q^2". 1 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
2
((9•(q2))-(—•(3q-7)))+5q2
3
STEP
2
:
2
Simplify —
3
Equation at the end of step
2
:
2
((9 • (q2)) - (— • (3q - 7))) + 5q2
3
STEP
3
:
Equation at the end of step 3
2 • (3q - 7)
((9 • (q2)) - ————————————) + 5q2
3
STEP
4
:
Equation at the end of step
4
:
2 • (3q - 7)
(32q2 - ————————————) + 5q2
3
STEP
5
:
Rewriting the whole as an Equivalent Fraction
5.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 3 as the denominator :
32q2 32q2 • 3
32q2 = ———— = ————————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
32q2 • 3 - (2 • (3q-7)) 27q2 - 6q + 14
——————————————————————— = ——————————————
3 3
Equation at the end of step
5
:
(27q2 - 6q + 14)
———————————————— + 5q2
3
STEP
6
:
Rewriting the whole as an Equivalent Fraction :
6.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 3 as the denominator :
5q2 5q2 • 3
5q2 = ——— = ———————
1 3
Trying to factor by splitting the middle term
6.2 Factoring 27q2 - 6q + 14
The first term is, 27q2 its coefficient is 27 .
The middle term is, -6q its coefficient is -6 .
The last term, "the constant", is +14
Step-1 : Multiply the coefficient of the first term by the constant 27 • 14 = 378
Step-2 : Find two factors of 378 whose sum equals the coefficient of the middle term, which is -6 .
-378 + -1 = -379
-189 + -2 = -191
-126 + -3 = -129
-63 + -6 = -69
-54 + -7 = -61
-42 + -9 = -51
For tidiness, printing of 26 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Adding fractions that have a common denominator :
6.3 Adding up the two equivalent fractions
(27q2-6q+14) + 5q2 • 3 42q2 - 6q + 14
—————————————————————— = ——————————————
3 3
STEP
7
:
Pulling out like terms :
7.1 Pull out like factors :
42q2 - 6q + 14 = 2 • (21q2 - 3q + 7)
Trying to factor by splitting the middle term
7.2 Factoring 21q2 - 3q + 7
The first term is, 21q2 its coefficient is 21 .
The middle term is, -3q its coefficient is -3 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant 21 • 7 = 147
Step-2 : Find two factors of 147 whose sum equals the coefficient of the middle term, which is -3 .
-147 + -1 = -148
-49 + -3 = -52
-21 + -7 = -28
-7 + -21 = -28
-3 + -49 = -52
-1 + -147 = -148
1 + 147 = 148
3 + 49 = 52
7 + 21 = 28
21 + 7 = 28
49 + 3 = 52
147 + 1 = 148
Observation : No two such factors can be found !!
Conclusion : Trinomial cannot be factored
Final result :
2 • (21q2 - 3q + 7)
———————————————————
3
